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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

In an equilat...

Question

In an equilateral triangle ABC, D is the midpoint of side BC. Prove that 4AD $^{2}$ = 3BC $^{2}$ .

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Solution

Let the side of triangle be $B C = a$
The height of Triangle $A D = \frac{\sqrt{3}}{2} a$
$4 A D^{2} = 4 {(\frac{\sqrt{3} a}{2})}^{2} 4 (\frac{3}{4} a^{2}) = 3 a^{2} = 3 B C^{2}$

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Q. In an equilateral

△ B A C

D

is the midpoint of side

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4 A D^{2} = 3 B C^{2}

△ A B C

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A C^{2} = 4 A D^{2} - 3 A B^{2}

Q. In an equilateral triangle

A B C

B C

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B D = \frac{1}{3} B C

9 A D^{2} = 7 A B^{2}

In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that 9 AD² = 7 AB².

Q. Question 15
In an equilateral triangle ABC, D is a point on side BC such that

B D = \frac{1}{3} B C

9 A D^{2} = 7 A B^{2}

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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

Standard IX Mathematics

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